APPLIED PROBABILITY FOR COMPUTER SCIENCE

This course is part of the required interdisciplinary activities of the Master's degree programme in Computer Science. Its aim is to provide the student with the fundamental tools of Probability and Statistics that are at the basis of data analysis in the presence of uncertainty. The student will acquire quantitative skills and knowledge of some of the basic probabilistic models and software used to describe and analyze relevant processes in the field of Computer Science, among others.

Attendance and participation in the training activities of the course, together with individual study will allow students to:

1. Knowledge and understanding:
- know and understand the probability models and statistical techniques that serve as a foundation for advanced methods of statistical learning and data analysis
- know and understand, in particular, Markovian probability models and the foundations of some stochastic processes

2. Ability to apply knowledge and understanding:
- use of specific programs for simulation and to calculate probabilities for the main families distributions
- capacity to autonomously analyze the properties of Markov chains, identifying their implications
- ability to apply estimation methods to solve some practical problems
- use of the appropriate formulas and terminology when applying and communicating the acquired knowledge

3. Ability to judge:
- contextualizing the acquired knowledge by identifying the most suitable models and methods for each situation

4. Communication skills:
- clear and exhaustive presentation of the results obtained as a solution to a probabilistic problem, using rigorous formulas and appropriate terminology

5. Learning skills:
- use and integrating information from notes, books, slides and practical sessions
- evaluation of the individual skills and preparation via quizzes and self-assessment exercises assigned during the course

Working differentiation and integration skills at the level of standard undergraduate calculus courses (a refresher, for reference purposes only is available in Section 12.3 of the textbook).

Basic matrix computations at the level of standard undergraduate linear algebra courses, in particular matrix multiplication and inversion and, solving linear systems of equations (a refresher, for reference purposes only is available in Section 12.4 of the textbook).

Basic knowledge of probability at the level of a Bachelor in Computer Science is advised. In particular, events, axioms of probability, conditional probability and independence, random variables, expected value, variance, covariance and correlation, main discrete and continuous distributions, central limit theorem, law of large numbers (these subjects, covered in chapters 2-3 of the textbook will be covered during the course at a deeper level)

1. Reminder of the basic concepts of Probability and Random Variables
- Axiomatic probability, conditional probability and independence
- Discrete Random Variables and Their Distributions
- Continuous Distributions
3. Stochastic Processes
- Markov processes and Markov chains
- Counting processes
- Continuous time Markov chains
- Poisson process
- Simulation of stochastic processes
4. Reminder of the basic concepts of Statistics
- Population and sample, parameters and statistics
- Descriptive statistics
5. Statistical Inference
- Parameter estimation
- Confidence intervals
- Hypothesis testing and Bayesian inference (if time allows it)

Main textbooks:
1. Probability and statistics for computer scientists. Baron, Michael, 2. ed. : Chapman & Hall/CRC, 2014
(Libro e-book available from the University Library System (SBA) https://www.unive.it/pag/9756/ )
2. Probability with Applications in Engineering, Science, and Technology. Carlton, Matthew A. and Devore, Jay L., 2 ed.: Springer, Cham, 2017
(e-book available on Springer-Link https://link.springer.com/book/10.1007/978-3-319-52401-6 )

Additional resources:
Additional suggested reading and materials made available on the Moodle platform

Achievement of the course objectives is evaluated through participation in activities and assignments during the course together with a team assignment and a written final exam.

The written final exam has a value of 25 points. The exercises are similar to those solved during the course or included in Moodle.
During the exam, the use of books, notes and calculator is allowed.
The use of the software R is an essential part of the program and is subject to examination.

The team assignment has a maximum value of 5 points. All team members will receive the same mark.

Students taking part in the activities and quizzes assigned during the classes may accumulate up to 3 extra points, to be added to the final written exam mark.

Any student with less than 5 points for the team assignment (including students not participating in the assignment) will have the opportunity to improve their grade, up to the maximum of 30 points by presenting an oral exam, only if they obtain full marks (25) for the written exam.

Theoretical lectures and exercises, including practical sessions using the software R. Use of Moodle platform for learning assessment.

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